1. Tell Google about your website (once).
When you’ve added a new website to the internet, there are two ways to tell Google that it exists: You can wait until another website (that Google does know about) links to you, or you can submit your site manually here: http://www.google.com/submityourcontent/website-owner/
2. Focus on adding quality content
Many new webmasters get so hung up on optimizing their site for search engines (a practice referred to as SEO for Search Engine Optimization) that they neglect the most important part of SEO: Writing fresh, quality content for the search engines to discover.
I have personally worked on many websites that enjoyed a #1 rank in Google for their target keywords, plus lots of organic (from Google) traffic on other keywords. If I could give you two rules for making it to the #1 spot in Google, they would be this: First, deserve it. Second, read SEOMoz.org.
If you dive deep into the world of SEO advice, and you really become an expert, it's possible to raise your rankings by tweaking the structure of your content, soliciting backlinks, etc. But the silver bullet for attracting traffic is creating really, really valuable content. You would do well to spend 75% percent of your time writing and building, and 25% tweaking for SEO (eventually your building and SEO process will overlap as you learn to "think in SEO").
3. Persist, especially when it gets boring.
For every five people I see succeed on the web, I see another ten completely give up. Building a great website takes a lot of time, like raising a child. Putting a couple weeks into a website and then asking "Why don't I have ten thousand uniques a day yet?" is like raising a child to age 2 and asking "Why isn't he a doctor yet?" Some days you're passionate and feel like working on your site; other days it feels like you'll never reach your online goals. It's important to work on your site regardless of your mood.
4. Set traffic goals.
When you're trying to lose weight, you might motivate yourself by setting a weight goal like, "I'm going to keep running and dieting until I'm down to 135lbs/62kg." You can do the same thing with your website. Don't set your goal too high. When I built my first website on my own (for myself, apart from a company), I remember being thrilled when my website would get 100 hits in a day. Now I feel (irrationally) dejected if it falls below fifty times that. Set your traffic goals in increments, and start small. Traffic can go up so gradually sometimes, but if you keep at it, you will reach your goals eventually.
5. Check stats every day.
There's a famous saying: "That which is measured, improves." You need to be a total web stats addict. I have two or three apps on my iPhone, a couple on my iPad, and of course Google Analytics on my desktop. If my brain has to go idle for than a couple minutes (e.g., waiting rooms, lines, long traffic lights), I'll check my site stats. It's kind of silly to be this obsessive, since gradual and abstracted stats trends are little more useful than daily hits, but it keeps me thinking about my sites, and also alerts me to problems (e.g., server outages) as well as sudden boosts from content that has gone viral.